Precalc

Question

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Let the vectors i and j be defined as usual:

$\mathbf{i} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}, \mathbf{j} = \begin{pmatrix} 0 \\ 1 \end{pmatrix}.$

Let A be a matrix such that Ai, Aj match the picture below:

Then for the vectors w,x,y and z above, calculate

$\mathbf{A}^{-1} \mathbf{w}, \mathbf{A}^{-1} \mathbf{x}, \mathbf{A}^{-1} \mathbf{y}, \mathbf{A}^{-1} \mathbf{z}$

and enter them in the order above. (Your answers should be numerical).

LearningCat May 31, 2024

nathanl6656 · Answer 1 · 2024-06-13T12:47:18

Here are the answers:

$\mathbf{A}^{-1} \mathbf{w} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$

$\mathbf{A}^{-1} \mathbf{x} = \begin{pmatrix} 4 \\ 0 \end{pmatrix}$

$\mathbf{A}^{-1} \mathbf{y} = \begin{pmatrix} -1 \\ 2 \end{pmatrix}$

$\mathbf{A}^{-1} \mathbf{z} = \begin{pmatrix} 5 \\ 1 \end{pmatrix}$